scholarly journals The Preconditioned SOR Iterative Method for Positive Definite Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yu-Qin Bai ◽  
Yan-Ping Xiao ◽  
Wei-Yuan Ma
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Positive Definite Matrices ◽  
Numerical Examples

We present several iterations for preconditioners introduced by Tarazaga and Cuellar (2009), and study the convergence of the method for solving a linear system whose coefficient matrix is positive definite matrices, and we also find that they complete very well with the SOR iteration, which is shown through numerical examples.

scholarly journals Least-squares fitting applied to nuclear mass formulas. Solution by the Gauss–Seidel method

2021 ◽  
Author(s):  
B. Mohammed-Azizi ◽  
H. Mouloudj
Keyword(s):  
Linear System ◽  
Least Squares ◽  
Statistical Data ◽  
Large Data ◽  
Positive Definite ◽  
Nuclear Mass ◽  
Positive Definite Matrices ◽  
Seidel Method ◽  
Semi Empirical ◽  
Mass Formulas

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

scholarly journals Convergence of the GAOR Method for One Subclass ofH-Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Ting Wang
Keyword(s):  
Linear System ◽  
Convergence Theorem ◽  
Coefficient Matrix ◽  
Linear Least Squares ◽  
Numerical Examples ◽  
Linear Least Squares Problem ◽  
Diagonally Dominant Matrix ◽  
Diagonally Dominant ◽  
Dominant Matrix ◽  
Better Than

We discuss the convergence of the GAOR method to solve linear system which occurred in solving the weighted linear least squares problem. Moreover, we present one convergence theorem of the GAOR method when the coefficient matrix is a strictly doublyαdiagonally dominant matrix which is a nonsingularH-matrix. Finally, we show that our results are better than previous ones by using four numerical examples.

Convergence of the Preconditioned AOR Method for an H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 2615-2619
Author(s):  
Jie Jing Liu
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Aor Method ◽  
Upper Triangular Matrix ◽  
Theoretical Results

Linear system with H-matrix often appears in a wide variety of areas and is studied by many numerical researchers. In order to improve the convergence rates of iterative method solving the linear system whose coefficient matrix is an H-matrix. In this paper, a preconditioned AOR iterative method with a multi-parameters preconditioner with a general upper triangular matrix is proposed. In addition, the convergence of the coressponding iterative method are established. Lastly, we provide numerical experiments to illustrate the theoretical results.

scholarly journals A New Version of the Accelerated Overrelaxation Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Shi-Liang Wu ◽  
Yu-Jun Liu
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Positive Definite ◽  
System Of Linear Equations ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Convergence Results ◽  
Aor Method ◽  
Symmetric Positive Definite Matrices ◽  
Overrelaxation Iterative Method

Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant,L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant,H-matrices, symmetric positive definite matrices, andL-matrices. A relational graph for the new AOR method and the original AOR method is presented. Finally, a numerical example is presented to illustrate the efficiency of the proposed method.

Convergence Results of the Improving Modified Gauss-Seidel (IMGS) Iterative Method for a Symmetric Positive Definite Matrix

2014 ◽  
Vol 989-994 ◽  
pp. 1794-1797
Author(s):  
Shi Guang Zhang ◽  
Ting Zhou
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Convergence Rates ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Symmetric Positive Definite Matrix ◽  
Symmetric Positive Definite ◽  
Convergence Results ◽  
Comparison Results

In this paper, in order to improve the convergence rates of iterative method solving the linear system, the improving modified Gauss-Seidel (IMGS) iterative method with a preconditioner is proposed. Some convergence and comparison results are given when is a symmetric definite matrix are provided.

A Preconditioned AOR Iterative Method for an H-Matrix

2014 ◽  
Vol 644-650 ◽  
pp. 1984-1987
Author(s):  
Shi Guang Zhang
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Triangular Matrix ◽  
Coefficient Matrix ◽  
Numerical Example ◽  
Upper Triangular Matrix

The paper presents a preconditioned AOR iterative method if preconditioner is a general upper triangular matrix for solving a linear system whose coefficient matrix is an H-matrix. In addition, we discuss the convergence of corresponding methods. Finally, a numerical example is also given to illustrate our results.

New Convergence of Relaxed Parallel Multisplitting Method for the H-Matrix

2013 ◽  
Vol 756-759 ◽  
pp. 3162-3166
Author(s):  
You Lin Zhang ◽  
Li Tao Zhang
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Iterative Method ◽  
Coefficient Matrix ◽  
Convergence Domain ◽  
Multisplitting Method ◽  
Multisplitting Methods ◽  
Relaxed Multisplitting Method

Relaxed technique is one of the main techniques for Improving convergence rate of splitting iterative method. Based on existing parallel multisplitting methods, we have deeply studied the convergence of the relaxed multisplitting method associated with TOR multisplitting for solving the linear system whose coefficient matrix is an H-matrix. Moreover, theoretical analysis have shown that the convergence domain of the relaxed parameters is weaker and wider.

SOME NEW COMPUTATIONAL METHODS TO SOLVE DUAL FULLY FUZZY LINEAR SYSTEM OF ARBITRARY TRIANGULAR FUZZY NUMBERS

2013 ◽  
Vol 09 (01) ◽  
pp. 13-26 ◽  
Author(s):  
AMIT KUMAR ◽  
BABBAR NEETU ◽  
ABHINAV BANSAL
Keyword(s):  
Linear System ◽  
Computational Methods ◽  
Fuzzy Numbers ◽  
Coefficient Matrix ◽  
Computational Techniques ◽  
Triangular Fuzzy Numbers ◽  
Numerical Examples ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Methods Numerical

In this paper, we discuss two new computational techniques for solving a generalized fully fuzzy linear system (FFLS) with arbitrary triangular fuzzy numbers (m,α,β). The methods eliminate the non-negative restriction on the fuzzy coefficient matrix that has been considered by almost every method in the literature and relies on the decomposition of the dual FFLS into a crisp linear system that can be further solved by a variety of classical methods. To illustrate the proposed methods, numerical examples are solved and the obtained results are discussed. The methods pose several advantages over the existing methods to solve a simple or dual FFLS.

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